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On the $W$-action on $B$-sheets in positive characteristic


Authors: Friedrich Knop and Guido Pezzini
Journal: Represent. Theory 19 (2015), 9-23
MSC (2010): Primary 20G15, 14M17, 14L30, 20G05
DOI: https://doi.org/10.1090/S1088-4165-2015-00464-9
Published electronically: March 6, 2015
MathSciNet review: 3318502
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Abstract: Let $G$ be a connected reductive group defined over an algebraically closed base field of characteristic $p\ge 0$, let $B\subseteq G$ be a Borel subgroup, and let $X$ be a $G$-variety. We denote the (finite) set of closed $B$-invariant irreducible subvarieties of $X$ that are of maximal complexity by $\mathfrak {B}_{0}(X)$. The first named author has shown that for $p=0$ there is a natural action of the Weyl group $W$ on $\mathfrak {B}_{0}(X)$ and conjectured that the same construction yields a $W$-action whenever $p\ne 2$. In the present paper, we prove this conjecture.


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Additional Information

Friedrich Knop
Affiliation: Department Mathematik, FAU Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
MR Author ID: 103390
ORCID: 0000-0002-4908-4060

Guido Pezzini
Affiliation: Department Mathematik, FAU Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
MR Author ID: 772887

Received by editor(s): September 2, 2013
Received by editor(s) in revised form: November 10, 2014, and February 3, 2015
Published electronically: March 6, 2015
Article copyright: © Copyright 2015 American Mathematical Society